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Computing Matrix Algebra with R and Rcpp

Matrix Inversion

Understand the concept of matrix inversion, its mathematical definition, and how to compute inverses in R using the solve() function. Explore coding the inversion algorithm using the adjugate method in C++ with Rcpp implementations. Compare results with RcppArmadillo and RcppEigen libraries to verify matrix inversions.

We'll cover the following...

Inverse definition

An (𝑛×𝑛)(𝑛 \times 𝑛) square matrix 𝐴𝐴 is called invertible (also nonsingular or nondegenerate) if there exists an (𝑛×𝑛)(𝑛 \times 𝑛) square matrix 𝐡𝐡 such that:

𝐴𝐡=𝐡𝐴=𝐼𝑛𝐴𝐡 = 𝐡𝐴 = 𝐼_𝑛

  • Here, 𝐼𝑛𝐼_𝑛 denotes the (𝑛×𝑛) ...